'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (120.8%) in the period of the last 5 years, the total return of 225.1% of ProShares Ultra Dow30 is greater, thus better.
- During the last 3 years, the total return is 71.1%, which is larger, thus better than the value of 66.3% from the benchmark.

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (17.2%) in the period of the last 5 years, the annual performance (CAGR) of 26.6% of ProShares Ultra Dow30 is greater, thus better.
- During the last 3 years, the compounded annual growth rate (CAGR) is 19.6%, which is larger, thus better than the value of 18.5% from the benchmark.

'Volatility is a rate at which the price of a security increases or decreases for a given set of returns. Volatility is measured by calculating the standard deviation of the annualized returns over a given period of time. It shows the range to which the price of a security may increase or decrease. Volatility measures the risk of a security. It is used in option pricing formula to gauge the fluctuations in the returns of the underlying assets. Volatility indicates the pricing behavior of the security and helps estimate the fluctuations that may happen in a short period of time.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (18.7%) in the period of the last 5 years, the historical 30 days volatility of 39.2% of ProShares Ultra Dow30 is larger, thus worse.
- During the last 3 years, the volatility is 47.2%, which is higher, thus worse than the value of 22.4% from the benchmark.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Which means for our asset as example:- Looking at the downside volatility of 28.4% in the last 5 years of ProShares Ultra Dow30, we see it is relatively greater, thus worse in comparison to the benchmark SPY (13.6%)
- Compared with SPY (16.3%) in the period of the last 3 years, the downside deviation of 34.1% is larger, thus worse.

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.78) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.61 of ProShares Ultra Dow30 is lower, thus worse.
- Looking at Sharpe Ratio in of 0.36 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.71).

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Applying this definition to our asset in some examples:- Looking at the excess return divided by the downside deviation of 0.85 in the last 5 years of ProShares Ultra Dow30, we see it is relatively lower, thus worse in comparison to the benchmark SPY (1.08)
- Looking at excess return divided by the downside deviation in of 0.5 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.98).

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Using this definition on our asset we see for example:- Looking at the Ulcer Index of 14 in the last 5 years of ProShares Ultra Dow30, we see it is relatively higher, thus worse in comparison to the benchmark SPY (5.59 )
- Looking at Ulcer Index in of 17 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (6.83 ).

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Which means for our asset as example:- Looking at the maximum DrawDown of -63.1 days in the last 5 years of ProShares Ultra Dow30, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum DrawDown is -63.1 days, which is smaller, thus worse than the value of -33.7 days from the benchmark.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Which means for our asset as example:- The maximum time in days below previous high water mark over 5 years of ProShares Ultra Dow30 is 248 days, which is higher, thus worse compared to the benchmark SPY (139 days) in the same period.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 248 days is larger, thus worse.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Applying this definition to our asset in some examples:- The average days below previous high over 5 years of ProShares Ultra Dow30 is 67 days, which is greater, thus worse compared to the benchmark SPY (33 days) in the same period.
- During the last 3 years, the average days under water is 78 days, which is greater, thus worse than the value of 35 days from the benchmark.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares Ultra Dow30 are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.